\[a^{m}_{n,k}(\gamma^{2})=(-1)^{k}\left(n+2k+\tfrac{1}{2}\right)\frac{(n-m+2k)!}%
{(n+m+2k)!}\*\int_{-1}^{1}\mathsf{Ps}^{m}_{n}\left(x,\gamma^{2}\right)\mathsf{%
P}^{m}_{n+2k}\left(x\right)\,\mathrm{d}x.\]